without loss of generality | Use of "without loss of generality&q

Keyword	CPC	PCC	Volume	Score	Length of keyword
without loss of generality	2	0.4	224	55	26
without	0.61	0.4	2613	55	7
loss	1.56	0.8	8550	90	4
of	1.77	0.8	5612	97	2
generality	2	0.1	4090	16	10

Keyword	CPC	PCC	Volume	Score
without loss of generality	1.47	0.6	7764	84

Search Results related to without loss of generality on Search Engine

Use of "without loss of generality" - Mathematics Stack Exchange
stackexchange.com

https://math.stackexchange.com/questions/129137/use-of-without-loss-of-generality

WEBApr 7, 2012 · For example: We want to show that P(x) P ( x) is true for all x ∈Z x ∈ Z. Without loss of generality, we can assume that x = z + 1 x = z + 1 for some z ∈Z z ∈ Z. [In this case, S =Z S = Z and T = {z + 1: z ∈ Z} T = { z + 1: z ∈ Z } .] We want to show that P(x) P ( x) is true for all x ∈Z x ∈ Z.

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Without loss of generality - Wikipedia
wikipedia.org

https://en.wikipedia.org/wiki/Without_loss_of_generality

WEBWithout loss of generality (often abbreviated to WOLOG, WLOG [1] or w.l.o.g.; less commonly stated as without any loss of generality or with no loss of generality) is a frequently used expression in mathematics. The term is used to indicate the assumption that follows is chosen arbitrarily, narrowing the premise to a particular case, but does ...

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terminology - "Without loss of generality" -- correct usage
stackexchange.com

https://math.stackexchange.com/questions/307204/without-loss-of-generality-correct-usage

WEB«Without loss of generality» is generally used when some minor, inconsequential change in notation allows one to add an assumption. It is also used to say that «with some work, we can see that...», and that is a more annoying usage.

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Without loss of generality - Art of Problem Solving
artofproblemsolving.com

https://artofproblemsolving.com/wiki/index.php/Without_loss_of_generality

WEBDefinition. Without loss of generality, often abbreviated to WLOG, is a frequently used expression in math. The term is used to indicate that the following proof emphasizes on a particular case, but doesn’t affect the validity of the proof in general. Be careful when using WLOG in a proof.

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elementary set theory - Proper use of "without loss of generality
stackexchange.com

https://math.stackexchange.com/questions/4154150/proper-use-of-without-loss-of-generality

WEBMay 28, 2021 · We say "without loss of generality" let's prove B B, when B ⇒ A B ⇒ A. – zkutch. May 28, 2021 at 15:49. 1. Suppose we were trying to prove the statement: for all real numbers a a and b b, |a + b| ≤ a + b. | a + b | ≤ a + b.

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Chapter 14 Without loss of generality | An Introduction to …
github.io

https://ijcwebb.github.io/proof/without-loss-of-generality.html

WEBChapter 14 Without loss of generality | An Introduction to Mathematical Proof. “Without loss of generality,” or simply w.l.o.g., is an incredibly useful technique which will save you a lot of time when using proof by cases. When used correctly, it allows you to merge two cases into one. Here’s a general example:

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How to explain the concept "Without loss of generality" (through …
stackexchange.com

https://matheducators.stackexchange.com/questions/25825/how-to-explain-the-concept-without-loss-of-generality-through-examples

WEBNov 22, 2022 · I got curious after a student of mine (in calculus I I ), while trying to prove that for every a ∈ R a ∈ R. (a +|a| 2)2 +(a − |a| 2)2 = a2, ( a + | a | 2) 2 + ( a − | a | 2) 2 = a 2, wrote that without loss of generality, we may assume that a ≥ 0 a ≥ 0. I decided not to accept this usage of the concept as legitimate.

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2.5: The Precise Definition of a Limit - Mathematics LibreTexts
libretexts.org

https://math.libretexts.org/Bookshelves/Calculus/Calculus_(OpenStax)/02%3A_Limits/2.05%3A_The_Precise_Definition_of_a_Limit

WEBSep 7, 2022 · Without loss of generality, assume \(ε≤4\). Two questions present themselves: Why do we want \(ε≤4\) and why is it okay to make this assumption? In answer to the first question: Later on, in the process of solving for \(δ\), we will discover that \(δ\) involves the quantity \(\sqrt{4−ε}\).

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What Does “Without Loss of Generality” Mean, and How Do …
springer.com

https://link.springer.com/content/pdf/10.1007/s11786-017-0316-2.pdf

WEBMany proofs, particularly of the more computational kind, in mathematics contain a line of the form “without loss of generality, we may assume …” (often abbreviated w.l.o.g). This is discussed in [6], who claims, we believe correctly, that this means one of two, rather different, types of argument:

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Without Loss of Generality - University of Cambridge
cam.ac.uk

https://www.cl.cam.ac.uk/~jrh13/papers/wlog.pdf

WEBWithout loss of generality, let a ≤ b ≤ c. If asked to spell this out in more detail, we might say something like: Since ≤ is a total order, the three numbers must be ordered somehow, i.e. we must have (at least) one of a ≤ b ≤ c, a ≤ c ≤ b, b …

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